Using vapor pressure to determine concentrations of components in a multi-component fluid

ABSTRACT

A system (700) for using a vapor pressure to determine a concentration of a component in a multi-component fluid is provided. The system (700) includes an electronics (710) communicatively coupled to a transducer (720) configured to sense a multi-component fluid. The electronics (710) is configured to determine a first vapor pressure, the first vapor pressure being a vapor pressure of a first component of the multi-component fluid, determine a second vapor pressure, the second vapor pressure being a vapor pressure of a second component of the multi-component fluid, and determine a multi-component vapor pressure, the multi-component vapor pressure being a vapor pressure of the multi-component fluid. The electronics (710) is also configured to determine a concentration of at least one of the first component and the second component based on the multi-component vapor pressure, the first vapor pressure, and the second vapor pressure.

TECHNICAL FIELD

The embodiments described below relate to determining a concentration ofa component in a multi-component fluid flow and, more particularly,using vapor pressure to determine concentrations of components in amulti-component fluid flow.

BACKGROUND

Vibrating sensors, such as for example, vibrating densitometers andCoriolis flowmeters are generally known, and are used to measure massflow and other information for materials flowing through a conduit inthe flowmeter. Exemplary Coriolis flowmeters are disclosed in U.S. Pat.Nos. 4,109,524, 4,491,025, and Re. 31,450, all to J. E. Smith et al.These flowmeters have one or more conduits of a straight or curvedconfiguration. Each conduit configuration in a Coriolis mass flowmeter,for example, has a set of natural vibration modes, which may be ofsimple bending, torsional, or coupled type. Each conduit can be drivento oscillate at a preferred mode.

Material flows into the flowmeter from a connected pipeline on the inletside of the flowmeter, is directed through the conduit(s), and exits theflowmeter through the outlet side of the flowmeter. The naturalvibration modes of the vibrating system are defined in part by thecombined mass of the conduits and the material flowing within theconduits.

When there is no-flow through the flowmeter, a driving force applied tothe conduit(s) causes all points along the conduit(s) to oscillate withidentical phase or a small “zero offset”, which is a time delay measuredat zero flow. As material begins to flow through the flowmeter, Coriolisforces cause each point along the conduit(s) to have a different phase.For example, the phase at the inlet end of the flowmeter lags the phaseat the centralized driver position, while the phase at the outlet leadsthe phase at the centralized driver position. Pickoffs on the conduit(s)produce sinusoidal signals representative of the motion of theconduit(s). Signals output from the pickoffs are processed to determinethe time delay between the pickoffs. The time delay between the two ormore pickoffs is proportional to the mass flow rate of material flowingthrough the conduit(s).

Meter electronics connected to the driver generate a drive signal tooperate the driver and determine a mass flow rate and other propertiesof a material from signals received from the pickoffs. The driver maycomprise one of many well-known arrangements; however, a magnet and anopposing drive coil have received great success in the flowmeterindustry. An alternating current is passed to the drive coil forvibrating the conduit(s) at a desired flow tube amplitude and frequency.It is also known in the art to provide the pickoffs as a magnet and coilarrangement very similar to the driver arrangement. However, while thedriver receives a current which induces a motion, the pickoffs can usethe motion provided by the driver to induce a voltage.

Vapor pressure is an important property in applications which handleflow and storage of volatile fluids such as gasoline, natural gasliquids, and liquid petroleum gas. Vapor pressure provides an indicationof how volatile fluids may perform during handling, and furtherindicates conditions under which bubbles will likely form and pressurewill likely build. As such, vapor pressure measurement of volatilefluids increases safety and prevents damage to transport vessels andinfrastructure. For example, if the vapor pressure of a fluid is toohigh, cavitation during pumping and transfer operations may occur.Furthermore, vessel or process line vapor pressure may potentially risebeyond safe levels due to temperature changes. It is therefore oftenrequired that vapor pressure be known prior to storage and transport.

In many applications it is desired to also know the concentrations ofcomponents in a multi-component fluid. This may require additionalequipment and/or laboratory samples. On-site measurement is morereliable, as it obviates the need for the periodic sampling and fullyeliminates the risk of fluid property changes between the time of samplecollection and laboratory assay. Furthermore, safety is improved byhaving real-time measurements, as unsafe conditions may be remediedimmediately. Additionally, money is saved, as regulatory enforcement maybe conducted via simple on-site checks, wherein inspection andenforcement decisions may be made with little delay or processcessation. Accordingly, it is desirable to determine the concentrationsof the components in the multi-component fluid by using vapor pressuresof the fluid.

SUMMARY

A system for using a vapor pressure to determine a concentration of acomponent in a multi-component fluid is provided. According to anembodiment, the system comprises an electronics communicatively coupledto a transducer configured to sense a multi-component fluid. Theelectronics is configured to determine a first vapor pressure, the firstvapor pressure being a vapor pressure of a first component of themulti-component fluid, determine a second vapor pressure, the secondvapor pressure being a vapor pressure of a second component of themulti-component fluid, determine a multi-component vapor pressure, themulti-component vapor pressure being a vapor pressure of themulti-component fluid, and determine a concentration of at least one ofthe first component and the second component based on themulti-component vapor pressure, the first vapor pressure, and the secondvapor pressure.

A method of using a vapor pressure to determine a concentration of acomponent in a multi-component fluid is provided. According to anembodiment, the method comprises determining a first vapor pressure, thefirst vapor pressure being a vapor pressure of a first component of themulti-component fluid, determining a second vapor pressure, the secondvapor pressure being a vapor pressure of a second component of themulti-component fluid, using a transducer having the multi-componentfluid to determine a multi-component vapor pressure, the multi-componentvapor pressure being a vapor pressure of the multi-component fluid, anddetermining a concentration of at least one of the first component andthe second component based on the multi-component vapor pressure, thefirst vapor pressure, and the second vapor pressure.

Aspects

According to an aspect, a system (700) for using a vapor pressure todetermine a concentration of a component in a multi-component fluidcomprises an electronics (710) communicatively coupled to a transducer(720) configured to sense a multi-component fluid. The electronics (710)is configured to determine a first vapor pressure, the first vaporpressure being a vapor pressure of a first component of themulti-component fluid, determine a second vapor pressure, the secondvapor pressure being a vapor pressure of a second component of themulti-component fluid, determine a multi-component vapor pressure, themulti-component vapor pressure being a vapor pressure of themulti-component fluid, and determine a concentration of at least one ofthe first component and the second component based on themulti-component vapor pressure, the first vapor pressure, and the secondvapor pressure.

Preferably, the electronics (710) being configured to determine theconcentration of at least one of the first component and the secondcomponent based on the multi-component vapor pressure, the first vaporpressure, and the second vapor pressure comprises the electronics (710)being configured to use equations:

P _(m) =P ₁ *x ₁ +P ₂ *x ₂; and

x ₁ +x ₂=1;

where:

-   -   P_(m) is the multi-component vapor pressure and is a sum of the        pressures exerted by each component of the multi-component fluid        being a two-component fluid;    -   P₁*, P₂* are respectively the first vapor pressure and the        second vapor pressure when the first component and the second        component are pure fluids; and    -   x₁, x₂ are respectively mole fractions of the first and second        component in the two-component fluid.

Preferably, the electronics (710) being configured to determine aconcentration of at least one of the first component and the secondcomponent based on the multi-component vapor pressure, the first vaporpressure, and the second vapor pressure comprises the electronics (710)being configured to determine the concentrations of the first component,the second component, and a third component using equations:

P_(m) = P₁^(*)x₁ + P₂^(*)x₂ + P₃^(*)x₃; x₁ + x₂ + x₃ = 1;MW_(mix) = x₁MW₁ + x₂MW₂ + x₃MW₃; and${\frac{1}{\rho_{T}} = {\frac{w_{1}}{\rho_{1}} + \frac{w_{2}}{\rho_{2}} + \frac{w_{3}}{\rho_{3}}}};$

where:

-   -   P_(m) is the multi-component vapor pressure of the        multi-component fluid where the multi-component fluid is a        three-component fluid;    -   x₁, x₂, and x₃ are respective mole fractions of the first        component, the second component, and the third component of the        three-component fluid;    -   P₁*, P₂*, and P₃* are respectively the first vapor pressure, the        second vapor pressure, and a third vapor pressure where the        first component, the second component, and the third component        are pure fluids;    -   MW_(mix) is a molecular weight of the three-component fluid;    -   MW₁, MW₂, and MW₃ are respective molecular weights of the first        component, the second component, and the third component;    -   w₁, w₂, and w₃ are respective mass fractions of the first        component, the second component, and the third component in the        three-component fluid and are respectively equal to        x₁MW₁/MW_(mix), x₂MW₂/MW_(mix), and x₃MW₃/MW_(mix);    -   ρ₁, ρ₂, and ρ₃ are respective densities of the first component,        the second component, and the third component of the        three-component fluid; and    -   ρ_(T) is a density of the three-component fluid.

Preferably, the electronics (710) is further configured to determine adensity of the multi-component fluid in the transducer (720) based onsensor signals provided by the transducer (720).

Preferably, the electronics (710) is further configured to determine atrue vapor pressure of the multi-component fluid based on a staticpressure of the multi-component fluid in the transducer (720).

Preferably, the electronics (710) is further configured to determine thevapor pressure based on a gain of a drive signal provided to thetransducer (720).

Preferably, the electronics (710) is a meter electronics (20) and thetransducer (720) is a meter assembly (10) of a vibratory meter (5).

According to an aspect, a method of using a vapor pressure to determinea concentration of a component in a multi-component fluid comprisesdetermining a first vapor pressure, the first vapor pressure being avapor pressure of a first component of the multi-component fluid,determining a second vapor pressure, the second vapor pressure being avapor pressure of a second component of the multi-component fluid, usinga transducer having the multi-component fluid to determine amulti-component vapor pressure, the multi-component vapor pressure beinga vapor pressure of the multi-component fluid, and determining aconcentration of at least one of the first component and the secondcomponent based on the multi-component vapor pressure, the first vaporpressure, and the second vapor pressure.

Preferably, determining the concentration of at least one of the firstcomponent and the second component based on the multi-component vaporpressure, the first vapor pressure, and the second vapor pressurecomprises using equations:

P _(m) =P ₁ *x ₁ +P ₂ *x ₂; and

x ₁ +x ₂=1;

where:

-   -   P_(m) is the multi-component vapor pressure and is a sum of the        pressures exerted by each component of the multi-component fluid        being a two-component fluid;    -   P₁*, P₂* are respectively the first vapor pressure and the        second vapor pressure when the first component and the second        component are pure fluids; and    -   x₁, x₂ are respectively mole fractions of the first and second        component in the two-component fluid.

Preferably, determining the concentration of at least one of the firstcomponent and the second component based on the multi-component vaporpressure, the first vapor pressure, and the second vapor pressurecomprises determining the concentrations of the first component, thesecond component, and a third component using equations:

P_(m) = P₁^(*)x₁ + P₂^(*)x₂ + P₃^(*)x₃; x₁ + x₂ + x₃ = 1;MW_(mix) = x₁MW₁ + x₂MW₂ + x₃MW₃; and${\frac{1}{\rho_{T}} = {\frac{w_{1}}{\rho_{1}} + \frac{w_{2}}{\rho_{2}} + \frac{w_{3}}{\rho_{3}}}};$

where:

-   -   P_(m) is the multi-component vapor pressure of the        multi-component fluid where the multi-component fluid is a        three-component fluid;    -   x₁, x₂, and x₃ are respective mole fractions of the first        component, the second component, and the third component of the        three-component fluid;    -   P₁*, P₂*, and P₃* are respectively the first vapor pressure, the        second vapor pressure, and a third vapor pressure where the        first component, the second component, and the third component        are pure fluids;    -   MW_(mix) is a molecular weight of the three-component fluid;    -   MW₁, MW₂, and MW₃ are respective molecular weights of the first        component, the second component, and the third component;    -   w₁, w₂, and w₃ are respective mass fractions of the first        component, the second component, and the third component in the        three-component fluid and are respectively equal to        x₁MW₁/MW_(mix), x₂MW₂/MW_(mix), and x₃MW₃/MW_(mix);    -   ρ₁, ρ₂, and ρ₃ are respective densities of the first component,        the second component, and the third component of the        three-component fluid; and    -   ρ_(T) is a density of the three-component fluid.

Preferably, the method further comprises determining a density of themulti-component fluid in the transducer based on sensor signals providedby the transducer.

Preferably, the method further comprises determining a true vaporpressure of the multi-component fluid based on a static pressure of themulti-component fluid in the transducer.

Preferably, the method further comprises determining the vapor pressurebased on a gain of a drive signal provided to the transducer.

Preferably, the transducer is a meter assembly of a vibratory meter.

BRIEF DESCRIPTION OF THE DRAWINGS

The same reference number represents the same element on all drawings.It should be understood that the drawings are not necessarily to scale.

FIG. 1 shows a vibratory meter 5.

FIG. 2 is a block diagram of the meter electronics 20 of vibratory meter5.

FIG. 3 shows a graph 300 illustrating a relationship between a drivegain and a gas-liquid ratio that can be used to determine a vaporpressure using a vapor pressure meter factor.

FIG. 4 shows a graph 400 illustrating how a static pressure of a fluidin a vibratory meter may be used to determine a vapor pressure.

FIG. 5 shows a system 500 for determining a vapor pressure of a fluid.

FIG. 6 shows a method 600 of using a vapor pressure to determine aconcentration of a component in a multi-component fluid.

FIG. 7 shows a system 700 for using a vapor pressure to determine aconcentration of a multi-component fluid.

DETAILED DESCRIPTION

FIGS. 1-7 and the following description depict specific examples toteach those skilled in the art how to make and use the best mode ofembodiments of using vapor pressure to determine concentrations ofcomponents in a multi-component fluid. For the purpose of teachinginventive principles, some conventional aspects have been simplified oromitted. Those skilled in the art will appreciate variations from theseexamples that fall within the scope of the present description. Thoseskilled in the art will appreciate that the features described below canbe combined in various ways to form multiple variations of using vaporpressure to determine the concentrations of the components in themulti-component fluid. As a result, the embodiments described below arenot limited to the specific examples described below, but only by theclaims and their equivalents.

FIG. 1 shows a vibratory meter 5. As shown in FIG. 1, the vibratorymeter 5 comprises a meter assembly 10 and meter electronics 20. Themeter assembly 10 responds to mass flow rate and density of a processmaterial. The meter electronics 20 is connected to the meter assembly 10via leads 100 to provide density, mass flow rate, temperatureinformation over path 26, and/or other information.

The meter assembly 10 includes a pair of manifolds 150 and 150′, flanges103 and 103′ having flange necks 110 and 110′, a pair of parallelconduits 130 and 130′, driver 180, resistive temperature detector (RTD)190, and a pair of pickoff sensors 170 l and 170 r. Conduits 130 and130′ have two essentially straight inlet legs 131, 131′ and outlet legs134, 134′, which converge towards each other at conduit mounting blocks120 and 120′. The conduits 130, 130′ bend at two symmetrical locationsalong their length and are essentially parallel throughout their length.Brace bars 140 and 140′ serve to define the axis W and W′ about whicheach conduit 130, 130′ oscillates. The legs 131, 131′ and 134, 134′ ofthe conduits 130, 130′ are fixedly attached to conduit mounting blocks120 and 120′ and these blocks, in turn, are fixedly attached tomanifolds 150 and 150′. This provides a continuous closed material paththrough meter assembly 10.

When flanges 103 and 103′, having holes 102 and 102′ are connected, viainlet end 104 and outlet end 104′ into a process line (not shown) whichcarries the process material that is being measured, material entersinlet end 104 of the meter through an orifice 101 in the flange 103 andis conducted through the manifold 150 to the conduit mounting block 120having a surface 121. Within the manifold 150 the material is dividedand routed through the conduits 130, 130′. Upon exiting the conduits130, 130′, the process material is recombined in a single stream withinthe mounting block 120′ having a surface 121′ and the manifold 150′ andis thereafter routed to outlet end 104′ connected by the flange 103′having holes 102′ to the process line (not shown).

The conduits 130, 130′ are selected and appropriately mounted to theconduit mounting blocks 120, 120′ so as to have substantially the samemass distribution, moments of inertia and Young's modulus about bendingaxes W-W and W′-W′, respectively. These bending axes go through thebrace bars 140, 140′. Inasmuch as the Young's modulus of the conduitschange with temperature, and this change affects the calculation of flowand density, RTD 190 is mounted to conduit 130′ to continuously measurethe temperature of the conduit 130′. The temperature of the conduit 130′and hence the voltage appearing across the RTD 190 for a given currentpassing therethrough is governed by the temperature of the materialpassing through the conduit 130′. The temperature dependent voltageappearing across the RTD 190 is used in a well-known method by the meterelectronics 20 to compensate for the change in elastic modulus of theconduits 130, 130′ due to any changes in conduit temperature. The RTD190 is connected to the meter electronics 20 by lead 195.

Both of the conduits 130, 130′ are driven by driver 180 in oppositedirections about their respective bending axes W and W′ and at what istermed the first out-of-phase bending mode of the flow meter. Thisdriver 180 may comprise any one of many well-known arrangements, such asa magnet mounted to the conduit 130′ and an opposing coil mounted to theconduit 130 and through which an alternating current is passed forvibrating both conduits 130, 130′. A suitable drive signal is applied bythe meter electronics 20, via lead 185, to the driver 180.

The meter electronics 20 receives the RTD temperature signal on lead195, and the left and right sensor signals appearing on leads 100carrying the left and right sensor signals 165 l, 165 r, respectively.The meter electronics 20 produces the drive signal appearing on lead 185to driver 180 and vibrate conduits 130, 130′. The meter electronics 20processes the left and right sensor signals and the RTD signal tocompute the mass flow rate and the density of the material passingthrough meter assembly 10. This information, along with otherinformation, is applied by meter electronics 20 over path 26 as asignal.

A mass flow rate measurement t can be generated according to theequation:

{dot over (m)}=FCF[Δt−×t ₀]  [1]

The Δt term comprises an operationally-derived (i.e., measured) timedelay value comprising the time delay existing between the pick-offsensor signals, such as where the time delay is due to Coriolis effectsrelated to mass flow rate through the vibratory meter 5. The measured Δtterm ultimately determines the mass flow rate of the flow material as itflows through the vibratory meter 5. The Δt₀ term comprises a time delayat zero flow calibration constant. The Δt₀ term is typically determinedat the factory and programmed into the vibratory meter 5. The time delayat zero flow Δt₀ term will not change, even where flow conditions arechanging. The flow calibration factor FCF is proportional to thestiffness of the vibratory meter 5.

Pressures in a Fluid in a Vibratory Meter

Assuming an incompressible liquid under steady conditions, the rate atwhich mass enters a control volume (e.g., a pipe) at an inlet ({dot over(m)}₁) equals the rate at which it leaves at an outlet ({dot over(m)}₃). This principle that the inlet mass flow rate ({dot over (m)}₁)must be equal to the outlet mass flow rate ({dot over (m)}₃) isillustrated by equation [2] below. Moving from the inlet to the outlet,the mass flow rate is conserved at each point along the pipe. However,there may be a reduction in a flow area midway between the inlet and theoutlet. This reduction in the flow area requires that the velocity ofthe fluid increase (ν↑) to maintain the same mass flow rate and obeyconservation of mass principles.

{dot over (m)} ₁=ρ₁ν₁ A ₁=ρ₂ν₂ A ₂ ={dot over (m)} ₂ ={dot over (m)}₃;  [2]

where:

{dot over (m)} is a mass flow rate of the fluid;

ν is an average fluid velocity;

ρ is a density of the fluid;

A is a total cross-sectional area;

subscript 1 indicates the inlet;

subscript 3 indicates the outlet; and

subscript 2 indicates midway between the inlet and the outlet.

Additionally, the total pressure in a flow system is equal to the sum ofboth the dynamic pressure and the static pressure:

P _(total) =P _(static) +P _(dynamic).  [3]

The dynamic pressure P_(dynamic) may be defined as:

$\begin{matrix}{{P_{dynamic} = \frac{\rho v^{2}}{2}};} & \lbrack 4\rbrack\end{matrix}$

where the terms ρ and ν are defined above with respect to equation [2].

Assuming steady, incompressible, inviscid, irrotational flow, theBernoulli equation gives:

$\begin{matrix}{{{Constant} = {\frac{\rho v^{2}}{2} + {\rho gz} + P}};} & \lbrack 5\rbrack\end{matrix}$

Where P refers to the static pressure and the ρgz term accounts forhydrostatic head due to elevation changes. More specifically, g is agravitational constant and z is a height. The viscous portion ofpressure drop can be handled with a separate loss term in the Bernoulliequation.

$\begin{matrix}{{{\Delta P_{viscous}} = {{- \frac{\rho v^{2}}{2}}\frac{fL}{D}}};} & \lbrack 6\rbrack\end{matrix}$

where;

f is a friction factor;

L is a length of a pipe; and

D is a diameter of the pipe.

The below equation [7] is a version of the Bernoulli equation thataccounts for frictional losses associated with traveling through a pipe.As fluid travels through the pipe, the fluid dissipates energy and thepressure drops across a given length of pipe. This loss in pressure isunrecoverable because energy from the fluid has been consumed throughfrictional losses. Accordingly, the following equation may account forthis loss:

$\begin{matrix}{{P_{1} + \frac{\rho v_{1}^{2}}{2} + {\rho gz_{1}} + {\Delta P_{viscous}}} = {P_{2} + \frac{\rho v_{2}^{2}}{2} + {\rho gz_{2}}}} & \lbrack 7\rbrack\end{matrix}$

This relationship can be applied to the exemplary pipe described abovewith reference to equation [2]. When the fluid moves from the inlet tomidway between the inlet and the outlet, there is a change in velocityto conserve the mass flow rate. Therefore, in maintaining therelationship shown in equation [7], the dynamic pressure

$\frac{\rho v^{2}}{2}$

increases, causing the static pressure to decrease. As the fluid movesto the outlet from midway between the inlet and outlet, the staticpressure is recovered through the same principles. That is, moving tothe outlet from midway between the inlet and the outlet, the flow areais increased; therefore, the fluid velocity is decreased, causing thedynamic pressure to decrease while recovering part of the initial staticpressure. However, the static pressure at the outlet will be lower dueto unrecoverable viscous losses.

This can cause the static pressures at the inlet and outlet to begreater than a vapor pressure of the fluid, while a static pressurebetween the inlet and outlet is less than the vapor pressure of thefluid. As a result, although the static pressures at the inlet and theoutlet are both greater than the vapor pressure of the fluid, flashingor outgassing may still occur in the pipe. Additionally, a vibratorymeter, such as a Coriolis meter, may be inserted into a pipeline thathas a diameter that is different than a diameter of a conduit orconduits in the vibratory meter. As a result, when outgassing isdetected in the vibratory meter, the pressure measured in the pipelinemay not be a vapor pressure of the fluid in the vibratory meter.

Meter Electronics—Drive Gain

FIG. 2 is a block diagram of the meter electronics 20 of vibratory meter5. In operation, the vibratory meter 5 provides various measurementvalues that may be outputted including one or more of a measured oraveraged value of mass flow rate, volume flow rate, individual flowcomponent mass and volume flow rates, and total flow rate, including,for example, both volume and mass flow of individual flow components.

The vibratory meter 5 generates a vibrational response. The vibrationalresponse is received and processed by the meter electronics 20 togenerate one or more fluid measurement values. The values can bemonitored, recorded, saved, totaled, and/or output. The meterelectronics 20 includes an interface 201, a processing system 203 incommunication with the interface 201, and a storage system 204 incommunication with the processing system 203. Although these componentsare shown as distinct blocks, it should be understood that the meterelectronics 20 can be comprised of various combinations of integratedand/or discrete components.

The interface 201 is configured to communicate with the meter assembly10 of the vibratory meter 5. The interface 201 may be configured tocouple to the leads 100 (see FIG. 1) and exchange signals with thedriver 180, pickoff sensors 170 l and 170 r, and RTDs 190, for example.The interface 201 may be further configured to communicate over thecommunication path 26, such as to external devices.

The processing system 203 can comprise any manner of processing system.The processing system 203 is configured to retrieve and execute storedroutines in order to operate the vibratory meter 5. The storage system204 can store routines including a flowmeter routine 205, a valvecontrol routine 211, a drive gain routine 213, and a vapor pressureroutine 215. The storage system 204 can store measurements, receivedvalues, working values, and other information. In some embodiments, thestorage system stores a mass flow (m) 221, a density (μ) 225, a densitythreshold 226, a viscosity (μ) 223, a temperature (T) 224, a pressure209, a drive gain 306, a drive gain threshold 302, a gas entrainmentthreshold 244, a gas entrainment fraction 248, and any other variablesknown in the art. The routines 205, 211, 213, 215 may comprise anysignal noted and those other variables known in the art. Othermeasurement/processing routines are contemplated and are within thescope of the description and claims.

As can be appreciated, more or fewer values may be stored in the storagesystem 204. For example, a vapor pressure may be determined withoutusing the viscosity 223. For example, estimate viscosity based on apressure drop, or a function relating friction as a function of flowrate. However, the viscosity 223 may be used to calculate a Reynoldsnumber which can then be used to determine a friction factor. TheReynolds number and friction factor can be employed to determine aviscous pressure drop in a conduit, such as the conduits 130, 130′described above with reference to FIG. 1. As can be appreciated, theReynolds number may not necessarily be employed.

The flowmeter routine 205 can produce and store fluid quantificationsand flow measurements. These values can comprise substantiallyinstantaneous measurement values or can comprise totalized oraccumulated values. For example, the flowmeter routine 205 can generatemass flow measurements and store them in the mass flow 221 storage ofthe storage system 204, for example. The flowmeter routine 205 cangenerate density 225 measurements and store them in the density 225storage, for example. The mass flow 221 and density 225 values aredetermined from the vibrational response, as previously discussed and asknown in the art. The mass flow and other measurements can comprise asubstantially instantaneous value, can comprise a sample, can comprisean averaged value over a time interval, or can comprise an accumulatedvalue over a time interval. The time interval may be chosen tocorrespond to a block of time during which certain fluid conditions aredetected, for example a liquid-only fluid state, or alternatively, afluid state including liquids and entrained gas. In addition, other massand volume flow and related quantifications are contemplated and arewithin the scope of the description and claims.

A drive gain threshold 302 may be used to distinguish between periods offlow, no flow, a monophasic/biphasic boundary (where a fluid phasechange occurs), and gas entrainment/mixed-phase flow. Similarly, adensity threshold 226 applied to the density reading 225 may also beused, separately or together with the drive gain, to distinguish gasentrainment/mixed-phase flow. Drive gain 306 may be utilized as a metricfor the sensitivity of the vibratory meter's 5 conduit vibration to thepresence of fluids of disparate densities, such as liquid and gasphases, for example, without limitation.

As used herein, the term drive gain refers to a measure of the amount ofpower needed to drive the flow tubes to specified amplitude, althoughany suitable definition may be employed. For example, the term drivegain may, in some embodiments, refer to drive current, pickoff voltage,or any signal measured or derived that indicates the amount of powerneeded to drive the flow conduits 130, 130′ at a particular amplitude.The drive gain may be used to detect multi-phase flow by utilizingcharacteristics of the drive gain, such as, for example, noise levels,standard deviation of signals, damping-related measurements, and anyother means known in the art to detect mixed-phase flow. These metricsmay be compared across the pick-off sensors 170 l and 170 r to detect amixed-phase flow.

Detecting a Phase Change of a Fluid

FIG. 3 shows a graph 300 illustrating a relationship between a drivegain and a gas-liquid ratio that can be used to determine a vaporpressure using a vapor pressure meter factor. As shown in FIG. 3, thegraph 300 includes an average void fraction axis 310 and a drive gainaxis 320. The average void fraction axis 310 and the drive gain axis 320are incremented in percentages, although any suitable units and/orratios may be employed.

The graph 300 includes plots 330 that are relationships between drivegains and gas-liquid ratios for various flow rates. As shown, thegas-liquid ratio is an average void fraction value of the plots 330,although any suitable gas-liquid ratio, such as a gas volume fraction(“GVF”) or a gas entrainment fraction, may be employed, and may be basedon volume, cross-sectional area, or the like. As can be appreciated, theplots 330 are similar despite being associated with different flowrates. Also shown is a drive gain threshold line 340 that intersectswith the plots 330 at about 0.20 percent average void fraction, whichmay be a reference average void fraction 330 a that corresponds to a 40%drive gain. Also shown is a true vapor pressure drive gain 332, which isabout 10%. The true vapor pressure drive gain 332 corresponds to thefluid in the meter assembly that has a static pressure at which a fluidphase change occurs and has a gas-liquid ratio of zero.

As can be seen, the plots 330 vary from a drive gain of about 10 percentto drive gain of about 100 percent over a range of average voidfractions from 0.00 percent to about 0.60 percent. As can beappreciated, a relatively small change in the average void fractionresults in a significant change in the drive gain. This relatively smallchange can ensure that the onset of vapor formation can be accuratelydetected with the drive gain.

Although the drive gain of 40% is shown as corresponding to an averagevoid fraction of 0.20 percent, the correspondence may be specific to aprocess. For example, the drive gain of 40% may correspond to otheraverage void fractions in other process fluids and conditions. Differentfluids may have different vapor pressures and therefore onset of vaporformation for the fluids may occur at different flow rates. That is, afluid with a relatively low vapor pressure will vaporize at higher flowrates and a fluid with relatively high vapor pressure may vaporize atlower flow rates.

As can also be appreciated, the drive gain threshold line 340 may be atalternative/other drive gains. However, it may be beneficial to have thedrive gain at 40% to eliminate false detections of entrainment/mixedphase flow while also ensuring that the onset of vapor formation iscorrectly detected.

Also, the plots 330 employ a drive gain, but other signals may be used,such as a measured density, or the like. The measured density mayincrease or decrease due to the presence of voids in the fluid. Forexample, the measured density may, counterintuitively, increase due tovoids in relatively high frequency vibratory meters because of avelocity-of-sound effect. In relatively low frequency meters, themeasured density may decrease due to the density of the voids being lessthan the fluid. These and other signals may be used alone or incombination to detect the presence of the vapor in the meter assembly.

As discussed above, the 0.20 percent average void fraction value may bethe reference average void fraction 330 a that corresponds to the 40percent drive gain value, which may be where the drive gain thresholdline 340 intersects with the drive gain axis 320. Accordingly, when ameasured drive gain is at 40 percent for a fluid in a meter assembly,such as the meter assembly 10 described above, then an average voidfraction of the fluid may be about 0.20 percent. The void fraction ofabout 0.20 percent may correspond to a pressure of the fluid due to gaspresent in the fluid. For example, the void fraction of about 0.20percent may correspond to, for example, a static pressure value.

Due to the previously determined relationship between the drive gain, orother signal, such as density, and the reference average void fraction330 a, which may be a reference gas-liquid ratio, a vapor pressure valuemay be associated with a vapor pressure meter factor. For example, themeter assembly may be vibrated while a static pressure is increased ordecreased until a fluid phase change is detected. A vapor pressure valuemay then be determined from the static pressure, as will be described inmore detail in the following with reference to FIG. 4. The determinedvapor pressure value may correspond to, for example, the static pressureat the drive gain threshold line 340. This determined vapor pressurevalue may be adjusted by the vapor pressure meter factor to correspondto the true vapor pressure drive gain 332, which is where a phase changeoccurs, or the monophasic/biphasic boundary is encountered. Accordingly,although the presence of gas in the fluid may be detected at a staticpressure that is different than the true vapor pressure of the fluid,the true vapor pressure value may nevertheless be determined.

Using the reference average void fraction 330 a as an example, thestatic pressure in the meter assembly may be reduced until the drivegain reaches 40 percent, thereby indicating that the fluid in the meterassembly has an average void fraction of 0.20 percent. A processingsystem, such as the processing system 203 described above, may determinethat the fluid began to vaporize at a static pressure that is, forexample, proportionally higher than the static pressure corresponding tothe 40 percent drive gain. For example, a true vapor pressure value maybe associated with a drive gain of about 10%. As can be appreciated, dueto uncertainties involved in calculating the static pressure (e.g.,errors from a pressure sensor, flow rate measurement errors, etc.) atrue vapor pressure may be proportionally lower than the calculatedstatic pressure that is associated with the 40% drive gain. True vaporpressure corresponds to a static pressure of the fluid where a fluidphase change occurs, but the gas-liquid ratio is zero.

Thus, the measured drive gain can be used to detect gas, yet still mayresult in a highly accurate true vapor pressure value. With moreparticularity, at the instant that outgassing first occurs, with a fewtiny bubbles present, drive gain may not increase past the drive gainthreshold line 340 for detection. A dynamic pressure may be increasedby, for example, a pump that continues to increase a flow rate until thestatic pressure drops such that drive gain passes the drive gainthreshold line 340. Depending on the application, this calculated staticpressure (e.g., an uncorrected vapor pressure) could be corrected (e.g.,adjusted—decreased or increased) by a vapor pressure meter factor of,for example, 1 psi, to account for the delay in detecting the fluidphase change. That is, the vapor pressure meter factor could bedetermined and applied to the uncorrected vapor pressure measurement asa function of drive gain to account for the difference in the drive gainat which the gas is detected and the true vapor pressure so as to detecttiny amounts of gas.

Referring to FIG. 3 by way of example, the measured drive gain of 40percent may correspond to a static pressure of the fluid in the meterassembly that is, for example, 1 psi less than a static pressurecorresponding to the drive gain associated with the true vapor pressure.Accordingly, the vibratory meter 5, or meter electronics 20, or anysuitable electronics, can determine that the vapor pressure meter factoris 1 psi and add this value from the static pressure associated with the40 percent drive gain. As a result, the vibratory meter 5 may accuratelydetect the phase change of the fluid and, therefore, also accuratelydetermine a vapor pressure of the fluid using the drive gain.

However, other means of detecting the phase change may be employed thatdo not use a drive gain. For example, the phase change may be detectedby acoustic measurement, x-ray-based measurements, optical measurements,etc. Also, combinations of the above implementations could beconsidered. For example, a bypass line that extends vertically in a loopwith acoustic and/or optical measurements distributed vertically todetermine where the gas first outgasses. This height would then providethe needed input to calculate a vapor pressure of the fluid in thevibratory meter 5, as the following explains.

Pressure Drop in a Vibratory Meter

FIG. 4 shows a graph 400 illustrating how a static pressure of a fluidin a vibratory meter may be used to determine a vapor pressure. As shownin FIG. 4, graph 400 includes a position axis 410 and a static pressureaxis 420. The position axis 410 is not shown with any particular unitsof length, but could be in units of inches, although any suitable unitmay be employed. The static pressure axis 420 is in units ofpounds-per-square inch (psi), although any suitable unit may beemployed. The position axis 410 ranges from an inlet (“IN”) to an outlet(“OUT”) of the vibratory meter.

Accordingly, the position from IN to OUT may correspond to fluid in, forexample, the meter assembly 10 shown in FIG. 1. In this example, theregion from IN to about A may correspond to a portion of the meterassembly 10 between the flange 103 to the conduit mounting block 120.The region from about A to about G may correspond to the conduits 130,130′ between the mounting blocks 120, 120′. The region from G to OUT maycorrespond to the portion of the meter assembly 10 from the mountingblock 120′ to the flange 103′. Accordingly, the fluid in the meterassembly 10 (e.g., in the position ranging from IN to OUT) may notinclude fluid in, for example, the pipeline in which the meter assembly10 is inserted. The fluid in the meter assembly 10 may be the fluid inthe conduits 130, 130′.

The graph 400 also includes a zero dynamic pressure plot 430 and adynamic pressure change plot 440. The zero dynamic pressure plot 430shows no change in the dynamic pressure—the pressure is assumed todecrease linearly from an inlet to an outlet of a vibratory meter. Thedynamic pressure change plot 440 may represent an actual pressure in thevibratory meter inserted into the pipeline wherein the diameter of theconduit or conduits of the vibratory meter is less than the diameter ofthe pipeline. An exemplary vibratory meter 5 is shown in FIG. 1,although any suitable vibratory meter may be employed. Accordingly, thefluid in the meter assembly, such as the meter assembly 10 describedabove, may have a reduced static pressure due to an increase in dynamicpressure. Also shown is a vapor pressure line 450 representing a vaporpressure of the fluid in the vibratory meter.

The dynamic pressure change plot 440 includes a static pressure dropsection 440 a, a viscous loss section 440 b, and a static pressureincrease section 440 c. The dynamic pressure change plot 440 alsoincludes a minimum static pressure 440 d. The static pressure dropsection 440 a may be due to an increase in fluid velocity causing acorresponding increase in the dynamic pressure of this section of thevibratory meter. The viscous loss section 440 b may correspond to aconstant diameter portion of the conduit or conduits in the vibratorymeter. Accordingly, the viscous loss section 440 b may not reflect anincrease in fluid velocity and, therefore, may not reflect an increasein a dynamic pressure. The static pressure increase section 440 c may bedue to a decrease in fluid velocity and, therefore, the static pressuredecrease during the static pressure drop section 440 a may be recovered.The static pressure drop section 440 a and the static pressure increasesection 440 c may be static pressure changes in the meter assembly.

The portion of the dynamic pressure change plot 440 lying below thevapor pressure line 450, which includes the minimum static pressure 440d, may correspond to positions (e.g., from about position E to slightlyafter position G) where a fluid phase change occurs in a fluid in ameter assembly, such as the meter assembly 10 described above. As can beseen in FIG. 4, the minimum static pressure 440 d is below the vaporpressure line 450. This indicates that the dynamic pressure change plot440 may be shifted upwards by increasing the static pressure of thefluid in the meter assembly. However, if the static pressure were to beincreased by about 5 psi so as to shift the dynamic pressure change plot440 up until the minimum static pressure 440 d lies on the vaporpressure line 450, a fluid phase change may be detected. Because thestatic pressure is increased, gas or vapor in the fluid in the meterassembly may become a liquid. Conversely, if the dynamic pressure changeplot 440 were above the vapor pressure line 450 and the static pressureof the fluid in the meter assembly were decreased until the minimumstatic pressure 440 d lies on the vapor pressure line, then the fluidphase change may be the formation of gas or vapor in the fluid.

As can be seen in FIG. 4, the viscous loss section 440 b decreases froma static pressure of about 68 psi at position A to a static pressure ofabout 55 psi at position G. As can be appreciated, the static pressureof about 55 psi at the position G is less than the vapor pressure line450, which is about 58 psi. As a result, even though the staticpressures at the inlet and outlet are greater than the vapor pressureline 450, the fluid in the vibratory meter may still flash or outgas.

Accordingly, the static pressure at the inlet and outlet do not directlycorrespond to the vapor pressure of the fluid. In other words, the vaporpressure of the fluid may not be directly determined from a staticpressure of the fluid in the pipeline or external of the meter assembly.The static pressure in the meter assembly 10 or, more specifically, theconduits 130, 130′, can be accurately determined by, for example, usingthe pressure measurements at the inlet and the outlet and inputting thedimensions of the vibratory meter 5 (e.g., diameter and length of theconduit 130, 130′). However, to accurately determine the vapor pressure,a phase change in the fluid in the vibratory meter 5 may need to beinduced, which may be caused by varying the static pressure of the fluidin the vibratory meter 5.

Varying a Static Pressure of a Fluid

FIG. 5 shows a system 500 for determining a vapor pressure of a fluid.As shown in FIG. 5, the system 500 is a bypass that includes a bypassinlet and a bypass outlet that are coupled to a pipeline 501. The system500 includes a pump 510 in fluid communication with an outlet of avibratory meter 5, illustrated as a Coriolis meter, and the bypassoutlet. An inlet pressure sensor 520 is in fluid communication with aninlet of the vibratory meter 5 and the bypass inlet. An outlet pressuresensor 530 is disposed between the outlet of the vibratory meter 5 andthe pump 510 and is configured to measure a static pressure of the fluidat the outlet of the vibratory meter 5. A flow control device 540, whichis shown as a valve, is disposed between the bypass inlet and the inletpressure sensor 520.

The pump 510 may be any suitable pump that can, for example, increase avelocity of the fluid in the vibratory meter 5. The pump 510 may, forexample, include a variable frequency drive. The variable frequencydrive may allow the pump 510 to control a fluid velocity of the fluid inthe system 500. For example, the variable frequency drive may increasethe fluid velocity of the fluid through the vibratory meter 5, althoughthe fluid velocity may be increased by any suitable pump. By increasingthe fluid velocity, the pump 510 can increase a dynamic pressure of thefluid in the vibratory meter 5 by increasing the fluid velocity.

Accordingly, the static pressure of the fluid in the vibratory meter 5may decrease. By way of illustration, with reference to FIG. 4, the pump510 may cause the dynamic pressure change plot 440 to shift downward.Accordingly, although not shown in FIG. 4, should the dynamic pressurechange plot 440 be above the vapor pressure line 450, the pump 510 mayinduce flashing or outgassing by causing the dynamic pressure changeplot 440 to shift downward. Similarly, by shifting the dynamic pressurechange plot 440 up to or above the vapor pressure line 450, gas or vaporin the fluid may become a liquid.

The inlet pressure sensor 520 and the outlet pressure sensor 530 may beany suitable pressure sensor configured to measure any pressure of thefluid. For example, the inlet pressure sensor 520 and the outletpressure sensor 530 may measure a static pressure of the fluid in thesystem 500. Additionally, or alternatively, the inlet pressure sensor520 and the outlet pressure sensor 530 may measure a total pressure ofthe fluid in the system 500. In one example, a dynamic pressure of thefluid may be determined by taking a difference between the totalpressure and the static pressure of the fluid in the system 500according to equation [3] above. For example, the inlet pressure sensor520 may measure the total pressure and the static pressure of the fluidproximate to, or at, an inlet of the vibratory meter 5. The inletpressure sensor 520 and/or the meter electronics 20 in the vibratorymeter 5 may determine the dynamic pressure at the inlet of the vibratorymeter 5.

The flow control device 540 may increase the fluid velocity of the fluidin the system 500 when the flow control device 540's position is movedfrom a partially closed position to a fully open position. For example,by decreasing flow restriction of the system 500 at the inlet of thevibratory meter 5, the velocity of the fluid may increase in accordancewith equation [2] above. This can shift the dynamic pressure change plot440 down so as to induce flashing or outgassing. Conversely, the flowcontrol device 540 can reduce the fluid velocity of the fluid in thesystem 500 thereby shifting the dynamic pressure change plot 440 up,thereby causing gas or vapors to condense.

As the flow control device 540 is opened, the fluid velocity willincrease, but so will a static pressure at the vibratory meter 5 inlet,and vice versa. The combination of the flow control device 540 with thepump 510 may provide a preferred process condition by partially closingthe flow control device 540 (e.g., to restrict a flow and lower pressuredownstream of the flow control device 540) and increasing pump speed(e.g., increasing flow rate) to obtain a desirably lower static pressureand higher velocity.

Although the static pressure of the fluid in the vibratory meter 5, or,more particularly, the meter assembly 10 in the vibratory meter 5, maybe varied by using the pump 510 or the flow control device 540, or acombination of both, described above, other means of varying the staticpressure may be employed. For example, a height z of the vibratory meter5 may be varied. To reduce the static pressure of the fluid in thevibratory meter 5, the height z may be increased. To increase the staticpressure of the fluid in the vibratory meter 5, the height z may bedecreased. The height z of the vibratory meter 5 may be varied by anysuitable means, such as a motorized lift between the vibratory meter 5and the pipeline 501 and bellows between the vibratory meter 5, forexample, the flow control device 540 and the pump 510. Other means maybe employed, as well as a combination of various means (e.g., the pump510, flow control device 540, and/or the motorized lift).

For example, if the flow rate through a bypass is sufficient, a pump maynot necessarily be employed. Only the flow control device 540 may beused. The flow control device 540 may be installed in other locations,such as downstream of the vibratory meter 5. Alternatively, the flowcontrol device 540 may not be employed, such as where the pump 510and/or motorized lift is used. In another alternative example, the metermay be installed in the main line, rather than a bypass. Additionally,or alternatively, only a single pressure sensor may be employed. Forexample, only the outlet pressure sensor 530 may be employed. The inletand/or outlet pressure sensors 520, 530 may be located at alternativelocations. The outlet pressure sensor 530 and its location may bebeneficial because the static pressure at the location of the outletpressure sensor 530 may substantially stabilize with respect to fluidvelocity once the fluid in the meter assembly 10 is at the vaporpressure. That is, any additional increase in the fluid velocity may notcause a substantial decrease in the static pressure measured by theoutlet pressure sensor 530.

Additional information can be inferred from the vapor pressuremeasurement. For example, if the flowing liquid is a mixture of two ormore pure substances, the vapor pressure can be used to estimate liquidphase concentrations of the pure components (i.e. component volume ormass fractions) using Dalton's and Raoult's Laws. Correlations forstandard hydrocarbons or other fluids could be put in the transmitterand added as a feature, similar to current concentration measurementcurves. Additionally, the concentration of salt, or other non-volatilesolutions can be determined. These concepts are explained in thefollowing:

Dalton's law of additive pressures, as expressed in equation [8], statesthat the total pressure exerted by a mixture of gases, P_(m) is equal tothe sum of the pressures exerted by each component of the mixture,P_(i), if each component existed separately at the same temperature andvolume as the mixture.

P _(m)=Σ_(i=1) ^(k) P _(i)  [8]

At the low pressures expected in the system 500 shown in FIG. 5, thebehavior of the gases can be assumed to approach ideal gas behaviorwhere Dalton's law best predicts the behavior of gas mixtures.

Raoult's law, as expressed in equation [9], states that the partialpressure of each component, P_(i), of an ideal mixture of liquids isequal to the vapor pressure of the pure component, P_(i)*, multiplied byits mole fraction in the liquid mixture or two-component fluid, x_(i).

P _(m) =P _(i) *x _(i)  [9]

Using the above equations and reference vapor pressure tables for purecomponents, the liquid concentrations for an ideal binary ortwo-component fluid can be obtained:

P _(m) =P ₁ *x ₁ +P ₂ *x ₂,  [10]

where:

-   -   P_(m), is the sum of the pressures exerted by each component of        the mixture and may be equal to a vapor pressure of the        multi-component fluid, such as a binary or two-component fluid;        and    -   P₁*x₁, P₂x₂ are respective partial pressures of the first and        second component in the two-component fluid.        As can be appreciated, due to the multi-component fluid being a        binary or two-component fluid, the first mole fraction x₁ is        equal to unity minus the second mole fraction x₂: 1−x₂. The        following example illustrates the use of the measured vapor        pressure to determine the liquid concentrations of a binary        mixture.

A liquid mixture of Benzene (B) and Toluene (T) flows through a processpipeline at 95° C. A portion of the liquid flows through a bypass linewhere the vapor pressure will be determined using a system like the oneproposed in this disclosure. The static pressure in the bypass systemdrops until the Coriolis meter detects the formation of gas bubbles. Themeasured vapor pressure at this point is 101.32 kPa. The followingillustrates how to determine the liquid concentration of each component.

A first step may be to find the vapor pressure of the pure components at95° C. This info can be found in the literature: P_(B)*=155.7 kPa;P_(T)*=63.3 kPa. The next step is to use Dalton's and Raoult's laws torelate the measured vapor pressure to liquid concentrations:

101.32 kPa=P _(B) +P _(T) =P _(B) *x _(B) +P _(T) *x _(T) =P _(B) *x_(B) +P _(T)*(1−x _(B))=155.7x _(B)+63.3(1−x _(B)).

Using a simple root finder, the mole fraction for Benzene can be solvedfor: x_(B)=0.411. Since x_(B)+x_(T)=1 it follows that x_(T)=0.589.

Using Density

The density measurement and the vapor pressure measurement can becombined to result in more equations and therefore be able to solve formore unknown components. Normally, if base densities of the purecompounds are known as a function of temperature, then the concentrationsoftware can accurately determine the volume fraction of up to twocomponents. However, with the addition of the vapor pressure informationdescribed above, three components can be differentiated, with componentvolume or mass fractions of each provided.

Allowing for determination of liquid fraction of three componentmixtures may increase the usable range of a concentration measurement ornet oil computer. The additional equations needed for three componentsare defined below, where (p refers to the volume fraction of eachcomponent and p is the density of each component, along with themeasured density.

φ₁+φ₂+φ₃=1  [11]

ρ₁φ₁+ρ₂φ₂+ρ₃φ₃=ρ_(measured)  [12]

By way of example, the following equation shows how the above Dalton'sand Raoult's laws can be used to determine a concentration of at leastone component in a multi-component fluid, the multi-component fluidbeing a three-component fluid.

P=P ₁ *x ₁ +P ₂ *x ₂ +P ₃ *x ₃;  [13]

where:

-   -   P is a vapor pressure of the three-component fluid, which may be        measured by a transducer;    -   x₁, x₂, and x₃ are mole fractions of the three components of the        three-component fluid; and    -   P₁*, P₂*, and P₃* are vapor pressures of each of the components        as a pure fluid; which may be known, for example, from a look-up        table.        The mole fractions of the three components x₁, x₂, x₃ may        necessarily add up to one:

x ₁ +x ₂ +x ₃=1.  [14]

In addition, the mole fractions of the three components x₁, x₂, x₃respectively multiplied by their molecular weight must sum to themolecular weight of the three-component fluid:

MW_(mix) =x ₁MW₁ +x ₂MW₂ +x ₃MW₃;  [15]

where:

-   -   MW_(mix) is a molecular weight of the three-component fluid; and    -   MW₁, MW₂, and MW₃ are molecular weights of each of the        components in the three-component fluid.        Additionally, an inverse of the density of the three-component        fluid may be equal to a sum of ratios of a mass fraction and a        density of each of the components in the three-component fluid:

$\begin{matrix}{{\frac{1}{\rho_{T}} = {\frac{w_{1}}{\rho_{1}} + \frac{w_{2}}{\rho_{2}} + \frac{w_{3}}{\rho_{3}}}};} & \lbrack 16\rbrack\end{matrix}$

where:

-   -   w₁, w₂, and w₃ are respective mass fractions of a first, second,        and third component in the three-component fluid and are        respectively equal to x₁MW₁/MW_(mix), x₂MW₂/MW_(mix), and        x₃MW₃/MW_(mix);    -   ρ₁, ρ₂, ρ₃ are respectively densities of the first, second, and        third component of the three-component fluid; and    -   ρ_(T) is a density of the three-component fluid, which may be        equal to the measured density ρ_(measured).        As can be appreciated, there are seven equations and seven        unknowns and therefore, the concentrations of each component may        be determined.

Even in mixtures with only two components, the vapor pressuremeasurement of the binary mixture can be used by itself to calculate thecomponent fractions of the mixture; this would be particularly useful incases where the densities of the pure components are equal, but theirvapor pressures are different. Alternatively, the vapor pressure of abinary mixture could be used to provide a secondary check for thedensity-based algorithms, even when the densities of the pure componentsare different.

Using a Vapor Pressure

FIG. 6 shows a method 600 of using a vapor pressure to determine aconcentration of a component in a multi-component fluid. As shown inFIG. 6, in step 610, the method 600 determines a first vapor pressure.The first vapor pressure is a vapor pressure of a first component of themulti-component fluid. In step 620, the method determines a second vaporpressure. The second vapor pressure is a vapor pressure of a secondcomponent of the multi-component fluid. In step 630, the methoddetermines a multi-component vapor pressure. The multi-component vaporpressure is a vapor pressure of the multi-component fluid. Themulti-component vapor pressure of the multi-component fluid may be a sumof the pressures exerted by each component in the multi-component fluid.The method 600, in step 640, determines a concentration of at least oneof the first component and the second component based on themulti-component vapor pressure, the first vapor pressure, and the secondvapor pressure.

In step 640, the method 600 can determine the concentration of the firstor the second component based on the multi-component vapor pressure, thefirst vapor pressure, and the second vapor pressure using above equation[10] as well as a mole fraction relationship of x₁+x₂=1. For athree-component fluid, the method 600 can determine the concentration ofthe first component, second component, and/or third component by usingequations [13]-[16] above.

The method 600 may also include additional steps. For example, themethod 600 may determine a density of the multi-component fluid in thetransducer based on sensor signals provided by the transducer. Forexample, the density may be determined by measuring a frequency, such asa resonant frequency, of the transducer and using a correlation betweenthe frequency and a density value to determine the density of themulti-component fluid. The method 600 may also further determine a truevapor pressure of the multi-component fluid based on a static pressureof the multi-component fluid in the transducer. The vapor pressure maybe determined based on a gain of the drive signal provided to thetransducer. The transducer may be the meter assembly of a vibratorymeter, although any suitable transducer may be employed, as thefollowing explains.

FIG. 7 shows a system 700 for using a vapor pressure to determine aconcentration of a multi-component fluid. As shown in FIG. 7, the system700 is comprised of an electronics 710 and a transducer 720. Theelectronics 710 may be configured to determine a vapor pressure of amulti-component fluid. For example, the electronics 710 may beconfigured to determine a first and a second vapor pressure, the firstand second vapor pressure being vapor pressures respectively of a firstcomponent and a second component of the multi-component fluid. Theelectronics 710 may also be configured to determine a multi-componentvapor pressure, where the multi-component vapor pressure is a vaporpressure of the multi-component fluid. The electronics 710 can use thevapor pressures to determine a concentration of the multi-componentfluid. For example, the electronics 710 may be configured to determine aconcentration of at least one of the first component and the secondcomponent based on the multi-component vapor pressure, the first vaporpressure, and the second vapor pressure.

The electronics 710 may also be configured to determine a density of themulti-component fluid. The density of the multi-component fluid may beequal to the sum of each density multiplied by the volume fraction ofeach component. For example, for a three-component fluid, the density ofthe three-component fluid may be equal to the sum of products of arespective density and volume fraction of the components in thethree-component fluid. The inverse of the density of the multi-componentfluid may be equal to a sum of respective mass fractions and densitiesof components in a multi-component fluid. For example, for athree-component fluid, the inverse of the density may be determinedaccording to above equation [16].

The above describes the vibratory meter 5, in particular the meterelectronics 20, and method 600, and system 700 using a vapor pressure todetermine a concentration of a component in a multi-component fluid. Theconcentration of the component may be determined using measurementsprovided by only the vibratory meter 5, although additional measurementsmay be made, such as the static pressure measurements described withreference to FIG. 5. As a result, information provided by the meterelectronics 20 may include not only mass flow rates and density, butalso concentrations of components in the multi-component fluid. Thefield of vibratory meters is improved because measurement capabilitiesof the vibratory meters are improved. Fields that employ vibratorymeters are also improved because the number of measurement devicesrequired to obtain the concentrations of components in a multi-componentfluid may be reduced, thereby saving costs. In addition, the informationmay be provided in real time and in situ thereby ensuring that the dataaccurately represents the multi-component fluid being measured.

The detailed descriptions of the above embodiments are not exhaustivedescriptions of all embodiments contemplated by the inventors to bewithin the scope of the present description. Indeed, persons skilled inthe art will recognize that certain elements of the above-describedembodiments may variously be combined or eliminated to create furtherembodiments, and such further embodiments fall within the scope andteachings of the present description. It will also be apparent to thoseof ordinary skill in the art that the above-described embodiments may becombined in whole or in part to create additional embodiments within thescope and teachings of the present description.

Thus, although specific embodiments are described herein forillustrative purposes, various equivalent modifications are possiblewithin the scope of the present description, as those skilled in therelevant art will recognize. The teachings provided herein can beapplied to other methods, electronics, systems, or the like for usingvapor pressure to determine concentrations of components in amulti-component fluid and not just to the embodiments described aboveand shown in the accompanying figures. Accordingly, the scope of theembodiments described above should be determined from the followingclaims.

We claim:
 1. A system (700) for using a vapor pressure to determine aconcentration of a component in a multi-component fluid, the system(700) comprising: an electronics (710) communicatively coupled to atransducer (720) configured to sense a multi-component fluid, theelectronics (710) being configured to: determine a first vapor pressure,the first vapor pressure being a vapor pressure of a first component ofthe multi-component fluid; determine a second vapor pressure, the secondvapor pressure being a vapor pressure of a second component of themulti-component fluid; determine a multi-component vapor pressure, themulti-component vapor pressure being a vapor pressure of themulti-component fluid; and determine a concentration of at least one ofthe first component and the second component based on themulti-component vapor pressure, the first vapor pressure, and the secondvapor pressure.
 2. The system (700) of claim 1, wherein the electronics(710) being configured to determine the concentration of at least one ofthe first component and the second component based on themulti-component vapor pressure, the first vapor pressure, and the secondvapor pressure comprises the electronics (710) being configured to useequations:P _(m) =P ₁ *x ₁ +P ₂ *x ₂; andx ₁ +x ₂=1; where: P_(m) is the multi-component vapor pressure and is asum of the pressures exerted by each component of the multi-componentfluid being a two-component fluid; P₁*, P₂* are respectively the firstvapor pressure and the second vapor pressure when the first componentand the second component are pure fluids; and x₁, x₂ are respectivelymole fractions of the first and second component in the two-componentfluid.
 3. The system (700) of claim 1, wherein the electronics (710)being configured to determine a concentration of at least one of thefirst component and the second component based on the multi-componentvapor pressure, the first vapor pressure, and the second vapor pressurecomprises the electronics (710) being configured to determine theconcentrations of the first component, the second component, and a thirdcomponent using equations: P_(m) = P₁^(*)x₁ + P₂^(*)x₂ + P₃^(*)x₃;x₁ + x₂ + x₃ = 1; MW_(mix) = x₁MW₁ + x₂MW₂ + x₃MW₃; and${\frac{1}{\rho_{T}} = {\frac{w_{1}}{\rho_{1}} + \frac{w_{2}}{\rho_{2}} + \frac{w_{3}}{\rho_{3}}}};$where: P_(m) is the multi-component vapor pressure of themulti-component fluid where the multi-component fluid is athree-component fluid; x₁, x₂, and x₃ are respective mole fractions ofthe first component, the second component, and the third component ofthe three-component fluid; P₁*, P₂*, and P₃* are respectively the firstvapor pressure, the second vapor pressure, and a third vapor pressurewhere the first component, the second component, and the third componentare pure fluids; MW_(mix) is a molecular weight of the three-componentfluid; MW₁, MW₂, and MW₃ are respective molecular weights of the firstcomponent, the second component, and the third component; w₁, w₂, and w₃are respective mass fractions of the first component, the secondcomponent, and the third component in the three-component fluid and arerespectively equal to x₁MW₁/MW_(mix), x₂MW₂/MW_(mix), andx₃MW₃/MW_(mix); ρ₁, ρ₂, and ρ₃ are respective densities of the firstcomponent, the second component, and the third component of thethree-component fluid; and ρ_(T) is a density of the three-componentfluid.
 4. The system (700) of claim 1, wherein the electronics (710) isfurther configured to determine a density of the multi-component fluidin the transducer (720) based on sensor signals provided by thetransducer (720).
 5. The system (700) of claim 1, wherein theelectronics (710) is further configured to determine a true vaporpressure of the multi-component fluid based on a static pressure of themulti-component fluid in the transducer (720).
 6. The system (700) ofclaim 1, wherein the electronics (710) is further configured todetermine the vapor pressure based on a gain of a drive signal providedto the transducer (720).
 7. The system (700) of claim 1, wherein theelectronics (710) is a meter electronics (20) and the transducer (720)is a meter assembly (10) of a vibratory meter (5).
 8. A method of usinga vapor pressure to determine a concentration of a component in amulti-component fluid, the method comprising: determining a first vaporpressure, the first vapor pressure being a vapor pressure of a firstcomponent of the multi-component fluid; determining a second vaporpressure, the second vapor pressure being a vapor pressure of a secondcomponent of the multi-component fluid; using a transducer having themulti-component fluid to determine a multi-component vapor pressure, themulti-component vapor pressure being a vapor pressure of themulti-component fluid; and determining a concentration of at least oneof the first component and the second component based on themulti-component vapor pressure, the first vapor pressure, and the secondvapor pressure.
 9. The method of claim 8, wherein determining theconcentration of at least one of the first component and the secondcomponent based on the multi-component vapor pressure, the first vaporpressure, and the second vapor pressure comprises using equations:P _(m) =P ₁ *x ₁ +P ₂ *x ₂; andx ₁ +x ₂=1; where: P_(m) is the multi-component vapor pressure and is asum of the pressures exerted by each component of the multi-componentfluid being a two-component fluid; P₁*, P₂* are respectively the firstvapor pressure and the second vapor pressure when the first componentand the second component are pure fluids; and x₁, x₂ are respectivelymole fractions of the first and second component in the two-componentfluid.
 10. The method of claim 8, wherein determining the concentrationof at least one of the first component and the second component based onthe multi-component vapor pressure, the first vapor pressure, and thesecond vapor pressure comprises determining the concentrations of thefirst component, the second component, and a third component usingequations: P_(m) = P₁^(*)x₁ + P₂^(*)x₂ + P₃^(*)x₃; x₁ + x₂ + x₃ = 1;MW_(mix) = x₁MW₁ + x₂MW₂ + x₃MW₃; and${\frac{1}{\rho_{T}} = {\frac{w_{1}}{\rho_{1}} + \frac{w_{2}}{\rho_{2}} + \frac{w_{3}}{\rho_{3}}}};$where: P_(m) is the multi-component vapor pressure of themulti-component fluid where the multi-component fluid is athree-component fluid; x₁, x₂, and x₃ are respective mole fractions ofthe first component, the second component, and the third component ofthe three-component fluid; P₁*, P₂*, and P₃* are respectively the firstvapor pressure, the second vapor pressure, and a third vapor pressurewhere the first component, the second component, and the third componentare pure fluids; MW_(mix) is a molecular weight of the three-componentfluid; MW₁, MW₂, and MW₃ are respective molecular weights of the firstcomponent, the second component, and the third component; w₁, w₂, and w₃are respective mass fractions of the first component, the secondcomponent, and the third component in the three-component fluid and arerespectively equal to x₁MW₁/MW_(mix), x₂MW₂/MW_(mix), andx₃MW₃/MW_(mix); ρ₁, ρ₂, and ρ₃ are respective densities of the firstcomponent, the second component, and the third component of thethree-component fluid; and ρ_(T) is a density of the three-componentfluid.
 11. The method of claim 8, further comprising determining adensity of the multi-component fluid in the transducer based on sensorsignals provided by the transducer.
 12. The method of claim 8, furthercomprising determining a true vapor pressure of the multi-componentfluid based on a static pressure of the multi-component fluid in thetransducer.
 13. The method of claim 8, further comprising determiningthe vapor pressure based on a gain of a drive signal provided to thetransducer.
 14. The method of claim 8, wherein the transducer is a meterassembly of a vibratory meter.